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Simplifying 0 = 60x3 + -240x2 + 240x Reorder the terms: 0 = 240x + -240x2 + 60x3 Solving 0 = 240x + -240x2 + 60x3 Solving for variable 'x'. Remove the zero: -240x + 240x2 + -60x3 = 240x + -240x2 + 60x3 + -240x + 240x2 + -60x3 Reorder the terms: -240x + 240x2 + -60x3 = 240x + -240x + -240x2 + 240x2 + 60x3 + -60x3 Combine like terms: 240x + -240x = 0 -240x + 240x2 + -60x3 = 0 + -240x2 + 240x2 + 60x3 + -60x3 -240x + 240x2 + -60x3 = -240x2 + 240x2 + 60x3 + -60x3 Combine like terms: -240x2 + 240x2 = 0 -240x + 240x2 + -60x3 = 0 + 60x3 + -60x3 -240x + 240x2 + -60x3 = 60x3 + -60x3 Combine like terms: 60x3 + -60x3 = 0 -240x + 240x2 + -60x3 = 0 Factor out the Greatest Common Factor (GCF), '60x'. 60x(-4 + 4x + -1x2) = 0 Factor a trinomial. 60x((-2 + x)(2 + -1x)) = 0 Ignore the factor 60.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, 2, 2}
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